# Caroline Aucoin

Geometry teacher | Verified Expert

I hold a degree in Geometry from Montclair State University. With a passion for unlocking the mysteries of shapes and spaces, I guide students through the intricacies of geometric concepts. My teaching style emphasizes clarity and practical application, empowering learners to excel in problem-solving and critical thinking. Drawing on my academic background and real-world experience, I foster a supportive learning environment where curiosity thrives. Together, we'll explore the fascinating world of geometry and uncover its relevance in everyday life. Let's embark on this journey of discovery together.

## Questions

What is an isosceles triangle?

An ellipsoid has radii with lengths of #9 #, #7 #, and #3 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

The radius of a circle is 2 inches. What is the circle's area?

What is the line of intersection between the planes #3x+y-4z=2# and #x+y=18#?

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #3 #, its base has sides of length #5 #, and its base has a corner with an angle of # pi/4 #. What is the pyramid's surface area?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #66 # and the height of the cylinder is #5 #. If the volume of the solid is #45 pi#, what is the area of the base of the cylinder?

What is the perimeter of a rectangle with sides 2/9 m and 5/6 m?

Given the similar right triangles in the figure. Find the exact values of x and y?

A triangle has corners at points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #11 #, what is the length of side BC?

Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 3 #. If one side of the triangle has a length of # 12 #, what is the longest possible perimeter of the triangle?

A rectangle has a perimeter of 50 cm. If the ratio of its length to its width is 3:2, find the length of the rectangle?

Two corners of a triangle have angles of # (7 pi )/ 12 # and # pi / 4 #. If one side of the triangle has a length of # 5 #, what is the longest possible perimeter of the triangle?

Circle A has a radius of #5 # and a center of #(2 ,6 )#. Circle B has a radius of #2 # and a center of #(4 ,3 )#. If circle B is translated by #<-3 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

What is value of x?

How to do this perpendicular bisector of a chord question?

What is the perimeter of a triangle with corners at #(1 ,8 )#, #(8 ,3 )#, and #(4 ,5 )#?

The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,1 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

A triangle has corners A, B, and C located at #(4 ,5 )#, #(3 ,6 )#, and #(2 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

Cups A and B are cone shaped and have heights of #34 cm# and #37 cm# and openings with radii of #12 cm# and #17 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

Which triangles in the figure above are congruent and/or similar? Find the value of x, angle #/_ACE# and the area #hat(AEC)#, and #BFDC#.